Superspace Unitary Operator in QED with Dirac and Complex Scalar Fields: Superfield Approach

We exploit the strength of the superspace (SUSP) unitary operator to obtain the results of the application of the horizontality condition (HC) within the framework of augmented version of superfield formalism that is applied to the interacting systems of Abelian 1-form gauge theories where the U(1) Abelian 1-form gauge field couples to the Dirac and complex scalar fields in the physical four (3 + 1)-dimensions of spacetime. These interacting theories are generalized onto a (4, 2)-dimensional supermanifold that is parametrized by the four (3 + 1)-dimensional (4D) spacetime variables and a pair of Grassmannian variables. To derive the (anti-)BRST symmetries for the matter fields, we impose the gauge invariant restrictions (GIRs) on the superfields defined on the (4, 2)-dimensional supermanifold. We discuss various outcomes that emerge out from our knowledge of the SUSP unitary operator and its hermitian conjugate. The latter operator is derived without imposing any operation of hermitian conjugation on the parameters and fields of our theory from outside. This is an interesting observation in our present investigation.Comment: LaTeX file, 11 pages, journal versio

Self-Dual Chiral Boson: Augmented Superfield Approach

We exploit the standard tools and techniques of the augmented version of Bonora-Tonin (BT) superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST and (anti-)co-BRST symmetry transformations for the Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density of a self-dual bosonic system. In the derivation of the full set of the above transformations, we invoke the (dual-)horizontality conditions, (anti-)BRST and (anti-)co-BRST invariant restrictions on the superfields that are defined on the (2, 2)-dimensional supermanifold. The latter is parameterized by the bosonic variable x^\mu\,(\mu = 0,\, 1) and a pair of Grassmanian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0 and \theta\bar\theta + \bar\theta\theta = 0). The dynamics of this system is such that, instead of the full (2, 2) dimensional superspace coordinates (x^\mu, \theta, \bar\theta), we require only the specific (1, 2)-dimensional super-subspace variables (t, \theta, \bar\theta) for its description. This is a novel observation in the context of superfield approach to BRST formalism. The application of the dual-horizontality condition, in the derivation of a set of proper (anti-)co-BRST symmetries, is also one of the new ingredients of our present endeavor where we have exploited the augmented version of superfield formalism which is geometrically very intuitive.Comment: LaTeX file, 27 pages, minor modifications, Journal reference is give

Curci-Ferrari Type Condition in Hamiltonian Formalism: A Free Spinning Relativistic Particle

The Curci-Ferrari (CF)-type of restriction emerges in the description of a free spinning relativistic particle within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism when the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations for this system are derived from the application of horizontality condition (HC) and its supersymmetric generalization (SUSY-HC) within the framework of superfield formalism. We show that the above CF-condition, which turns out to be the secondary constraint of our present theory, remains time-evolution invariant within the framework of Hamiltonian formalism. This time-evolution invariance (i) physically justifies the imposition of the (anti-)BRST invariant CF-type condition on this system, and (ii) mathematically implies the linear independence of BRST and anti-BRST symmetries of our present theory.Comment: LaTeX file, 11 Pages, journal versio

Ab initio Wannier-function-based correlated calculations of Born effective charges of crystalline Li2_{2}O and LiCl

In this paper we have used our recently developed ab initio Wannier-function-based methodology to perform extensive Hartree-Fock and correlated calculations on Li$_{2}$O and LiCl to compute their Born effective charges. Results thus obtained are in very good agreement with the experiments. In particular, for the case of Li$_{2}$O, we resolve a controversy originating in the experiment of Osaka and Shindo {[}Solid State Commun. 51 (1984) 421] who had predicted the effective charge of Li ions to be in the range 0.58--0.61, a value much smaller compared to its nominal value of unity, thereby, suggesting that the bonding in the material could be partially covalent. We demonstrate that effective charge computed by Osaka and Shindo is the Szigeti charge, and once the Born charge is computed, it is in excellent agreement with our computed value. Mulliken population analysis of Li$_{2}$O also confirms ionic nature of the bonding in the substance.Comment: 11 pages, 1 figure. To appear in Phys. Rev. B (Feb 2008

Novel symmetries in the modified version of two dimensional Proca theory

By exploiting Stueckelberg's approach, we obtain a gauge theory for the two (1+1)-dimensional (2D) Proca theory and demonstrate that this theory is endowed with, in addition to the usual Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries, the on-shell nilpotent (anti-)co-BRST symmetries, under which the total gauge-fixing term remains invariant. The anticommutator of the BRST and co-BRST (as well as anti-BRST and anti-co-BRST) symmetries define a unique bosonic symmetry in the theory, under which the ghost part of the Lagrangian density remains invariant. To establish connections of the above symmetries with the Hodge theory, we invoke a pseudo-scalar field in the theory. Ultimately, we demonstrate that the full theory provides a field theoretic example for the Hodge theory where the continuous symmetry transformations provide a physical realization of the de Rham cohomological operators and discrete symmetries of the theory lead to the physical realization of the Hodge duality operation of differential geometry. We also mention the physical implications and utility of our present investigation.Comment: LaTeX file, 21 pages, journal referenc

Supervariable Approach to the Nilpotent Symmetries for a Toy Model of the Hodge Theory

We exploit the standard techniques of the supervariable approach to derive the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a toy model of the Hodge theory (i.e., a rigid rotor) and provide the geometrical meaning and interpretation to them. Furthermore, we also derive the nilpotent (anti-)co-BRST symmetry transformations for this theory within the framework of the above supervariable approach. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian of our present theory within the framework of augmented supervariable formalism. We also express the (anti-)BRST and (anti-)co-BRST charges in terms of the supervariables (obtained after the application of the (dual-)horizontality conditions and (anti-)BRST and (anti-)co-BRST invariant restrictions) to provide the geometrical interpretations for their nilpotency and anticommutativity properties. The application of the dual-horizontality condition and ensuing proper (i.e., nilpotent and absolutely anticommuting) fermionic (anti-)co-BRST symmetries are completely novel results in our present investigation

Inversion of moments to retrieve joint probabilities in quantum sequential measurements

A sequence of moments encode the corresponding probability distribution. Probing if quantum joint probability distribution can be retrieved from the associated set of moments -- realized in the sequential measurement of a dichotomic observable at different time intervals -- reveals a negative answer i.e., the joint probabilities of sequential measurements do not agree with the ones obtained by inverting the moments. This is indeed a reflection of the non-existence of a bonafide grand joint probability distribution, consistent with all the physical marginal probability distributions. Here we explicitly demonstrate that given the set of moments, it is not possible to retrieve the three-time quantum joint probability distribution resulting from quantum sequential measurement of a single qubit dichotomic observable at three different times. Experimental results using a nuclear magnetic resonance (NMR) system are reported here to corroborate these theoretical observations viz., the incompatibility of the three-time joint probabilties with those extracted from the moment sequence.Comment: 7 pages, 5 figures, RevTe

Nonlinear excitation of zonal flows by rossby wave turbulence

We apply the wave-kinetic approach to study nonlinearly coupled Rossby wave-zonal flow fluid turbulence in a two-dimensional rotating fluid. Specifically, we consider for the first time nonlinear excitations of zonal flows by a broad spectrum of Rossby wave turbulence. Short-wavelength Rossby waves are described here as a fluid of quasi-particles, and are referred to as the 'Rossbyons'. It is shown that Reynolds stresses of Rossbyons can generate large-scale zonal flows. The result should be useful in understanding the origin of large-scale planetary and near-Earth atmospheric circulations. It also provides an example of a turbulent wave background driving a coherent structure

Hysteresis in Random Field XY and Heisenberg Models: Mean Field Theory and Simulations at Zero Temperature

We examine zero temperature hysteresis in random field XY and Heisenberg models in the zero frequency limit of a cyclic driving field. Exact expressions for hysteresis loops are obtained in the mean field approximation. These show rather unusual features. We also perform simulations of the two models on a simple cubic lattice and compare them with the predictions of the mean field theory.Comment: replaced by the published versio

Gibbs energies of formation of rare earth oxysulfides

The standard Gibbs energy change accompanying the conversion of rare earth oxides to oxysulfides by reaction of rare earth oxides with diatomic sulfur gas has been measured in the temperature range 870 to 1300 K using the solid state cell: Pt/Cu+Cu2S/R2O2S+R2O3||(CaO)ZrO2||Ni+NiO, Pt where R=La, Nd, Sm, Gd, Tb, and Dy. The partial pressure of diatomic sulfur over a mixture of rare earth oxide (R2O3) and oxysulfide (R2O2S) is fixed by the dissociation of Cu2S to Cu in a closed system. The buffer mixture of Cu+Cu2S is physically separated from the rare earth oxide and oxysulfide to avoid complications arising from interaction between them. The corresponding equilibrium oxygen partial pressure is measured with an oxide solid electrolyte cell. Gibbs energy change for the conversion of oxide to the corresponding oxysulfide increases monotonically with atomic number of the rare earth element. Second law enthalpy of formation also shows a similar trend. Based on this empirical trend Gibbs energies of formation of oxysulfides of Pr, Eu, Ho, and Er are estimated as a function of temperature